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Valuation of Equity-Indexed Annuities Under Stochastic Interest Rates

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  • X. Sheldon Lin
  • Ken Seng Tan

Abstract

This paper considers the pricing of equity-indexed annuities (EIAs). Traditionally, the values of the guarantees embedded in these contracts are priced by modeling the underlying index fund while keeping the interest rates constant. The assumption of constant interest rates becomes unrealistic in pricing and hedging the EIAs since the embedded guarantees are often of much longer maturity. To solve this problem, the authors propose an economic model that has the flexibility of modeling the underlying index fund as well as the interest rates. Some popular EIAs are illustrated to assess the implication of the proposed model.

Suggested Citation

  • X. Sheldon Lin & Ken Seng Tan, 2003. "Valuation of Equity-Indexed Annuities Under Stochastic Interest Rates," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 72-91.
    • Handle: RePEc:taf:uaajxx:v:7:y:2003:i:4:p:72-91
    DOI: 10.1080/10920277.2003.10596119
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    Cited by:

    1. Charles Guy Njike Leunga & Donatien Hainaut, 2022. "Valuation of Annuity Guarantees Under a Self-Exciting Switching Jump Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 963-990, June.
    2. Yuanchuang Shan & Huisheng Shu & Haoran Yi, 2023. "Pricing Equity-Indexed Annuities under a Stochastic Dividend Model," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    3. Thorsten Moenig, 2022. "It's RILA time: An introduction to registered index‐linked annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(2), pages 339-369, June.
    4. Feng, Runhuan & Shimizu, Yasutaka, 2016. "Applications of central limit theorems for equity-linked insurance," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 138-148.
    5. Kijima, Masaaki & Wong, Tony, 2007. "Pricing of Ratchet equity-indexed annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 317-338, November.
    6. Risk, J. & Ludkovski, M., 2016. "Statistical emulators for pricing and hedging longevity risk products," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 45-60.
    7. Günther, Sascha & Hieber, Peter, 2024. "Analyzing the interest rate risk of equity-indexed annuities via scenario matrices," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 15-28.
    8. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    9. Coleman, Thomas F. & Li, Yuying & Patron, Maria-Cristina, 2006. "Hedging guarantees in variable annuities under both equity and interest rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 215-228, April.
    10. Ballotta, Laura & Eberlein, Ernst & Schmidt, Thorsten & Zeineddine, Raghid, 2021. "Fourier based methods for the management of complex life insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 320-341.
    11. Qian, Linyi & Wang, Wei & Wang, Rongming & Tang, Yincai, 2010. "Valuation of equity-indexed annuity under stochastic mortality and interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 123-129, October.
    12. Gao, Quansheng & He, Ting & Zhang, Chi, 2011. "Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy," Economic Modelling, Elsevier, vol. 28(1), pages 147-156.
    13. Dai, Tian-Shyr & Yang, Sharon S. & Liu, Liang-Chih, 2015. "Pricing guaranteed minimum/lifetime withdrawal benefits with various provisions under investment, interest rate and mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 364-379.
    14. Moore, Kristen S., 2009. "Optimal surrender strategies for equity-indexed annuity investors," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 1-18, February.
    15. Pansera, Jérôme, 2012. "Discrete-time local risk minimization of payment processes and applications to equity-linked life-insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 1-11.
    16. Richter, Andreas & Weber, Frederik, 2009. "Mortality-Indexed Annuities," Discussion Papers in Business Administration 10994, University of Munich, Munich School of Management.
    17. Chiu, Yu-Fen & Hsieh, Ming-Hua & Tsai, Chenghsien, 2019. "Valuation and analysis on complex equity indexed annuities," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    18. Maciej Augustyniak & Mathieu Boudreault, 2017. "Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(4), pages 502-525, October.
    19. Gao, Quansheng & He, Ting & Zhang, Chi, 2011. "Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy," Economic Modelling, Elsevier, vol. 28(1-2), pages 147-156, January.
    20. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Pricing annuity guarantees under a double regime-switching model," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 62-78.
    21. Chen, Hua & Cox, Samuel H. & Wang, Shaun S., 2010. "Is the Home Equity Conversion Mortgage in the United States sustainable? Evidence from pricing mortgage insurance premiums and non-recourse provisions using the conditional Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 371-384, April.
    22. Liew, Chuin Ching & Siu, Tak Kuen, 2010. "A hidden Markov regime-switching model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 374-384, December.
    23. Paolo Angelis & Roberto Marchis & Antonio L. Martire & Emilio Russo, 2022. "A flexible lattice framework for valuing options on assets paying discrete dividends and variable annuities embedding GMWB riders," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 415-446, June.
    24. Seo, Jun-Ho & Kim, Jeong-Hoon, 2022. "Multiscale stochastic elasticity of variance for options and equity linked annuity; A Mellin transform approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 303-320.
    25. Wei, Jiaqin & Wang, Rongming & Yang, Hailiang, 2012. "Optimal surrender strategies for equity-indexed annuity investors with partial information," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1251-1258.

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